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Cell["\<\
\:041f\:043e\:043b\:0443\:0447\:0435\:043d\:0438\:0435 \:0441\:0438\:0441\
\:0442\:0435\:043c\:044b \:0434\:043b\:044f \:043d\:0430\:0445\:043e\:0436\
\:0434\:0435\:043d\:0438\:044f \:0438\:043d\:043a\:0440\:0435\:043c\:0435\
\:043d\:0442\:043e\:0432\
\>", "Subsection"],

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Cell["\<\
\:041f\:043e\:043b\:0443\:0447\:0435\:043d\:0438\:0435 \:0431\:0430\:0437\
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\:043d\:0443\:043b\:0438 \:0411\:0435\:0441\:0441\:0435\:043b\:044f)\
\>", "Subsubsection"],

Cell[BoxData[
    \(<< NumericalMath`BesselZeros`\)], "Input"],

Cell[BoxData[
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        If[ir \[Equal] 0, 0  KroneckerDelta[ir, i\[Phi]], 
          Last[Evaluate[BesselJZeros[i\[Phi], ir]]]]\)\)], "Input"],

Cell[CellGroupData[{

Cell["\:041f\:0440\:043e\:0432\:0435\:0440\:043a\:0438", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
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        16.470630050877634`}, {5.135622301840683`, 8.417244140399873`, 
        11.619841172149059`, 14.79595178235126`, 
        17.959819494987826`}, {6.380161895923984`, 9.761023129981625`, 
        13.015200721698434`, 16.223466160318768`, 
        19.409415226435012`}, {7.588342434503804`, 11.064709488501176`, 
        14.37253667161759`, 17.615966049804832`, 
        20.826932956962388`}, {8.771483815959943`, 12.338604197466944`, 
        15.70017407971167`, 18.98013387517992`, 
        22.217799896561267`}}\)], "Output"]
}, Open  ]],

Cell[BoxData[
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        ir = 10}, \(Plot[
          BesselJ[i\[Phi], bz[i\[Phi], ir] r], {r, 0, 1}];\)]\)], "Input"]
}, Closed]]
}, Open  ]],

Cell[CellGroupData[{

Cell["\:0412\:044b\:0434\:0435\:043b\:0435\:043d\:0438\:0435 \:043a\:043e\
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"Subsubsection"],

Cell[BoxData[{
    \(BesselNorm[i\[Phi]_, ir_] := 
      If[ir \[Equal] 0, 
        KroneckerDelta[ir, i\[Phi]]\/2, \((BesselJ[\(-1\) + i\[Phi], bz[i\
\[Phi], ir]] - BesselJ[1 + i\[Phi], bz[i\[Phi], ir]])\)\^2\/8 + \((1 - 
                i\[Phi]\^2\/ir\^2)\) 
            BesselJ[i\[Phi], bz[i\[Phi], ir]]\^2\/2]\), \
"\[IndentingNewLine]", 
    \( (*\[Integral]\+0\%1 
            r\ \(BesselJ[i\[Phi], 
                  bz[i\[Phi], ir] 
                    r]\^2\) \[DifferentialD]r\ \((\:043d\:0435\ \:043f\:0440\
\:0438\:043c\:0435\:043d\:044f\:0442\:044c\ \:0432\ \:0441\:0438\:043c\:0432\
\:043e\:043b\:044c\:043d\:043e\:043c\ \(\:0432\:0438\:0434\:0435!\) 
                bz\ \:0433\:043b\:044e\:0447\:0438\:0442)\)\  - \ \
\:0442\:043e\ \:0436\:0435\ \:0441\:0430\:043c\:043e\:0435, \ \:043d\:043e\ \
\:0434\:043e\:043b\:044c\:0448\:0435*) \)}], "Input"],

Cell[BoxData[
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        If[if1 \[Equal] if2, KroneckerDelta[ir1, ir2] BesselNorm[if1, ir1], 
          NIntegrate[
            r\ BesselJ[if1, bz[if1, ir1] r] BesselJ[if2, bz[if2, ir2] r], {r, 
              0, 1}]];\)\)], "Input"],

Cell[BoxData[
    \(\(\( (*n = i\[Phi], 
      mun = \(\[Mu]\_n = ir\)*) \)\(\[IndentingNewLine]\)\(GetHarmCoef[expr_, 
        i\[Phi]_, ir_] := 
      Block[{\[Rho], \[Phi]}, \(1\/\(2  \[Pi]\ BesselNorm[i\[Phi], 
                  ir]\)\) \(\[Integral]\+0\%1\(\[Integral]\+0\%\(2  \[Pi]\)\
\[Rho]\ expr\ BesselJ[i\[Phi], 
                  bz[i\[Phi], 
                      ir]\ \[Rho]]\ \(E\^\(\(-\[ImaginaryI]\)\ i\[Phi]\ \
\[Phi]\)\) \[DifferentialD]\[Phi] \[DifferentialD]\[Rho]\)\)]\)\)\)], "Input"],

Cell[BoxData[
    \(GetHarmCoef[expr_, i\[Phi]_, ir_] := 
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          NIntegrate[\[Rho]\ expr\ BesselJ[i\[Phi], 
                bz[i\[Phi], 
                    ir]\ \[Rho]]\ E\^\(\(-\[ImaginaryI]\)\ i\[Phi]\ \[Phi]\), \
{\[Phi], 0, 2  \[Pi]}, {\[Rho], 0, 1}]]\)], "Input"],

Cell[BoxData[
    \(\(GetHarmCoef[expr_, i\[Phi]_, ir_] := 
        Block[{\[Rho], \[Phi], vir, opts}, \[IndentingNewLine]Off[
            NIntegrate::"\<ploss\>"]; \[IndentingNewLine]vir = 
            Chop[\[Integral]\+0\%\(2  \[Pi]\)expr\ \(E\^\(\(-\[ImaginaryI]\)\ \
i\[Phi]\ \[Phi]\)\) \[DifferentialD]\[Phi]]; \[IndentingNewLine]opts = 
            Sequence[MaxRecursion \[Rule] 20]; \[IndentingNewLine]Return[
            Expand[\(1\/\(2  \[Pi]\ BesselNorm[i\[Phi], ir]\)\) 
                  vir\ BesselJ[i\[Phi], 
                    bz[i\[Phi], ir] \[Rho]] \[Rho]] /. {BesselJ[i1_, 
                      k1_\ \[Rho]] 
                    BesselJ[i2_, k2_\ \[Rho]] \[Rho]\^por_.  \[RuleDelayed] 
                  NIntegrate[
                    BesselJ[i1, k1\ \[Rho]] 
                      BesselJ[i2, k2\ \[Rho]] \[Rho]\^por, {\[Rho], 0, 1}, 
                    Evaluate[opts]], 
                BesselJ[i1_, k1_\ \[Rho]] 
                    BesselJ[i2_, k2_\ \[Rho]] \[RuleDelayed] 
                  NIntegrate[
                    BesselJ[i1, k1\ \[Rho]] BesselJ[i2, k2\ \[Rho]], {\[Rho], 
                      0, 1}, Evaluate[
                      opts]], \(BesselJ[i1_, 
                          k1_\ \[Rho]]\^2\) \[Rho]\^por_.  \[RuleDelayed] 
                  NIntegrate[\(BesselJ[i1, 
                            k1\ \[Rho]]\^2\) \[Rho]\^por, {\[Rho], 0, 1}, 
                    Evaluate[opts]], 
                BesselJ[i1_, k1_\ \[Rho]]\^2 \[RuleDelayed] 
                  NIntegrate[BesselJ[i1, k1\ \[Rho]]\^2, {\[Rho], 0, 1}, 
                    Evaluate[opts]], 
                a_.  BesselJ[i1_, k1_\ \[Rho]] \[RuleDelayed] 
                  NIntegrate[a\ BesselJ[i1, k1\ \[Rho]], {\[Rho], 0, 1}, 
                    Evaluate[opts]]}]; \[IndentingNewLine]On[
            NIntegrate::"\<ploss\>"];\[IndentingNewLine]];\)\)], "Input"],

Cell[CellGroupData[{

Cell["\:041f\:0440\:043e\:0432\:0435\:0440\:043a\:0438", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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        0.04503473245716366`, 0.031176262813236297`}, {0.`, 
        0.05768742740874397`, 0.03682425491868484`, 
        0.027014904075039866`}, {0.`, 0.04448348887831025`, 
        0.031104368944316556`, 0.023822869521262894`}}\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
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              BesselJ[i\[Phi], bz[i\[Phi], ir] \[Rho]] 
              E\^\(\[ImaginaryI]\ i\[Phi]\ \[Phi]\)\), 1, 2] // 
      Chop\)], "Input"],

Cell[BoxData[
    RowBox[{\(NIntegrate::"ploss"\), \(\(:\)\(\ \)\), "\<\"Numerical \
integration stopping due to loss of precision. Achieved neither the requested \
PrecisionGoal nor AccuracyGoal; suspect one of the following: highly \
oscillatory integrand or the true value of the integral is 0. If your \
integrand is oscillatory on a (semi-)infinite interval try using the option \
Method->Oscillatory in NIntegrate. \
\\!\\(\\*ButtonBox[\\\"More\[Ellipsis]\\\", ButtonStyle->\\\"RefGuideLinkText\
\\\", ButtonFrame->None, ButtonData:>\\\"NIntegrate::ploss\\\"]\\)\"\>"}]], \
"Message"],

Cell[BoxData[
    RowBox[{\(NIntegrate::"slwcon"\), \(\(:\)\(\ \)\), "\<\"Numerical \
integration converging too slowly; suspect one of the following: singularity, \
value of the integration being 0, oscillatory integrand, or insufficient \
WorkingPrecision. If your integrand is oscillatory try using the option \
Method->Oscillatory in NIntegrate. \
\\!\\(\\*ButtonBox[\\\"More\[Ellipsis]\\\", ButtonStyle->\\\"RefGuideLinkText\
\\\", ButtonFrame->None, ButtonData:>\\\"NIntegrate::slwcon\\\"]\\)\"\>"}]], \
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Cell[BoxData[
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integration stopping due to loss of precision. Achieved neither the requested \
PrecisionGoal nor AccuracyGoal; suspect one of the following: highly \
oscillatory integrand or the true value of the integral is 0. If your \
integrand is oscillatory on a (semi-)infinite interval try using the option \
Method->Oscillatory in NIntegrate. \
\\!\\(\\*ButtonBox[\\\"More\[Ellipsis]\\\", ButtonStyle->\\\"RefGuideLinkText\
\\\", ButtonFrame->None, ButtonData:>\\\"NIntegrate::ploss\\\"]\\)\"\>"}]], \
"Message"],

Cell[BoxData[
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Cell[CellGroupData[{

Cell["\<\
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Cell[BoxData[
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Cell[BoxData[
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\\!\\(0.4999998092651367`\\). Continuing to refine elsewhere. \
\\!\\(\\*ButtonBox[\\\"More\[Ellipsis]\\\", ButtonStyle->\\\"RefGuideLinkText\
\\\", ButtonFrame->None, \
ButtonData:>\\\"FunctionInterpolation::ncvb\\\"]\\)\"\>"}]], "Message"]
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Cell[BoxData[
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Cell[BoxData[
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Cell[CellGroupData[{

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Cell[CellGroupData[{

Cell["\<\
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\:043b\:043e\:0436\:0435\:043d\:0438\:044f \:043f\:043e \:0446\:0438\:043b\
\:0438\:043d\:0434\:0440\:0438\:0447\:0435\:0441\:043a\:0438\:043c \:0433\
\:0430\:0440\:043c\:043e\:043d\:0438\:043a\:0430\:043c\
\>", "Subsubsection"],

Cell[CellGroupData[{

Cell["\<\
\:041c\:043d\:043e\:0436\:0438\:0442\:0435\:043b\:044c \:0434\:043b\:044f \
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\>", "Text"],

Cell[BoxData[
    \(\[Rho]\^Exponent[eqs\[Phi]r[\[Lambda], 0, 0, \[Kappa], G, Re], \[Rho]\^\
\(-1\)]\)], "Input"]
}, Closed]],

Cell[BoxData[
    \(\(\( (*\:0422 . \:043a . \ \:0443\ v\[Zeta]\ \:043c\:0430\:043a\:0441\
\:0438\:043c\:0443\:043c\ 2\ \:043f\:0440\:043e\:0438\:0437\:0432\:043e\:0434\
\:043d\:0430\:044f\ \:043f\:043e\ \[Rho], \ \:0430\ \:0443\ \[Psi]\ \:043c\
\:0430\:043a\:0441\:0438\:043c\:0443\:043c\ 4, \ \:0442\:043e\ \:0444\:0438\
\:043a\:0442\:0438\:0432\:043d\:044b\:0435\ \:0441\:043b\:043e\:0438\  - \ \
\:0443\ v\[Zeta] \((f)\) = 1, \ \:0443\ \[Psi] \((g)\) = 
        2*) \)\(\[IndentingNewLine]\)\(SpectralMatrix4Eigen[nr_, n\[Phi]_, 
          subst___] := 
        Block[{\[Rho], unk, systcf, cfs, v, \[Psi]c, vir, \[Rho]mul, lhs, 
            rhs}, \[IndentingNewLine]\[Rho]mul = 
            Exponent[
              eqs\[Phi]r[\[Lambda], 0, 0, \[Kappa], G, 
                Re], \[Rho]\^\(-1\)]; \[IndentingNewLine]vir = \(\[Rho]\^\
\[Rho]mul\) ReplaceAll[
                eqs\[Phi]r[\[Lambda], \[Omega], \[Epsilon], \[Kappa], G, 
                  Re], {v\[Zeta] \[Rule] 
                    Function[{\[Rho], \[Phi]}, \[Sum]\+\(ir = 1\)\%nr\(\[Sum]\
\+\(i\[Phi] = 0\)\%n\[Phi]\( v\_\(ir, i\[Phi]\)\) 
                            BesselJ[i\[Phi], bz[i\[Phi], ir] \[Rho]] 
                            E\^\(\[ImaginaryI]\ i\[Phi]\ \[Phi]\)\)], \[Psi] \
\[Rule] Function[{\[Rho], \[Phi]}, \[Sum]\+\(ir = 1\)\%nr\(\[Sum]\+\(i\[Phi] \
= 0\)\%n\[Phi]\( \[Psi]c\_\(ir, i\[Phi]\)\) 
                            BesselJ[i\[Phi], bz[i\[Phi], ir] \[Rho]] 
                            E\^\(\[ImaginaryI]\ i\[Phi]\ \[Phi]\)\)], 
                  subst}]; \[IndentingNewLine]unk = 
            Flatten[Table[{v\_\(ir, i\[Phi]\), \[Psi]c\_\(ir, i\[Phi]\)}, \
{ir, 1, nr}, {i\[Phi], 0, n\[Phi]}]]; \[IndentingNewLine]systcf = 
            Outer[D[#1, #2] &, vir, unk]; \[IndentingNewLine]cfs = 
            Map[Flatten[
                  Table[GetHarmCoef[#, i\[Phi], ir], {ir, nr}, {i\[Phi], 0, 
                      n\[Phi]}]] &, systcf, {2}]; \[IndentingNewLine]cfs = 
            Flatten /@ 
              Transpose[cfs]; \[IndentingNewLine]lhs = \(-Coefficient[
                cfs, \[Lambda], 1]\); \[IndentingNewLine]rhs = 
            Coefficient[cfs, \[Lambda], 0]; \[IndentingNewLine]Return[{lhs, 
              rhs}];\[IndentingNewLine]];\)\)\)], "Input",
  InitializationCell->True]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
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          0, 0.07534763452515092`\ \[Kappa], 
          2.13639412842478`}}, {{1.2610619876489286`\/Re, \
\(0.5549151430289984`\ \[Kappa]\)\/Re - 
            0.00011557657604602885`\ G\^2\ Re\ \[Kappa] - 
            0.0007658929011329671`\ G\ Re\ \[Kappa]\ \[Omega], 
          0, \(-0.1047431358676974`\)\ \[ImaginaryI]\ G\ \[Kappa] - 
            0.585395247901433`\ \[ImaginaryI]\ \[Kappa]\ \[Omega]}, {0, 
          0.0030698132999111283`\ \[ImaginaryI]\ G\ \[Kappa] - 
            4.157325349219731`*^-6\ \[ImaginaryI]\ G\^3\ Re\^2\ \[Kappa] - 
            0.03277718988478524`\ \[ImaginaryI]\ Re\ \[Epsilon]\ \[Kappa] - 
            1.109830286057997`\ \[ImaginaryI]\ \[Kappa]\ \[Omega] - 
            0.000027164252792063974`\ \[ImaginaryI]\ G\^2\ Re\^2\ \[Kappa]\ \
\[Omega], 
          2.653649615928378`\/Re, \(3.385449580439322`\ \[Kappa]\)\/Re + 
            6.972702837207759`*^-6\ G\^2\ Re\ \[Kappa] + 
            0.0005244416001394039`\ G\ Re\ \[Kappa]\ \[Omega]}, \
{\(0.02710921267809349`\ \[Kappa]\)\/Re - 
            0.00006568002178707814`\ G\^2\ Re\ \[Kappa] - 
            0.00040545391664440714`\ G\ Re\ \[Kappa]\ \[Omega], 
          4.893990214041299`\/Re, 
          0.03433072433772288`\ \[ImaginaryI]\ G\ \[Kappa] + 
            0.15069526905030184`\ \[ImaginaryI]\ \[Kappa]\ \[Omega], 
          0}, {\(-0.048344149057053885`\)\ \[ImaginaryI]\ G\ \[Kappa] + 
            1.907691318680299`*^-6\ \[ImaginaryI]\ G\^3\ Re\^2\ \[Kappa] + 
            0.009689975253410067`\ \[ImaginaryI]\ Re\ \[Epsilon]\ \[Kappa] + 
            0.05421842535618698`\ \[ImaginaryI]\ \[Kappa]\ \[Omega] + 
            0.000012178767275970296`\ \[ImaginaryI]\ G\^2\ Re\^2\ \[Kappa]\ \
\[Omega], 
          0.1666666666666667`\ \[ImaginaryI]\ G, \(2.212503516103493`\ \
\[Kappa]\)\/Re + 0.0002476649474886485`\ G\^2\ Re\ \[Kappa] + 
            0.0015469650912364437`\ G\ Re\ \[Kappa]\ \[Omega], 
          31.36647587353848`\/Re}}}\)], "Output"]
}, Open  ]]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Map[Coefficient[#, \[Lambda], 1] &, 
      Last[Out[223]] + \[Lambda]\ First[Out[223]], {0}]\)], "Input"],

Cell[BoxData[
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        0.2926976239507165`\ \[Kappa]}, {0, 0.3333333333333334`, 0, 0}, {0, 
        0, 0.07534763452515092`\ \[Kappa], 2.13639412842478`}}\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
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{0, \(-0.3333333333333334`\), 0, 0}, {0, 
          0, \(-0.07534763452515092`\)\ \[Kappa], \(-2.13639412842478`\)}}, \
{{1.2610619876489286`\/Re, \(0.5549151430289984`\ \[Kappa]\)\/Re - 
            0.00011557657604602885`\ G\^2\ Re\ \[Kappa] - 
            0.0007658929011329671`\ G\ Re\ \[Kappa]\ \[Omega], 
          0, \(-0.1047431358676974`\)\ \[ImaginaryI]\ G\ \[Kappa] - 
            0.585395247901433`\ \[ImaginaryI]\ \[Kappa]\ \[Omega]}, {0, 
          0.0030698132999111283`\ \[ImaginaryI]\ G\ \[Kappa] - 
            4.157325349219731`*^-6\ \[ImaginaryI]\ G\^3\ Re\^2\ \[Kappa] - 
            0.03277718988478524`\ \[ImaginaryI]\ Re\ \[Epsilon]\ \[Kappa] - 
            1.109830286057997`\ \[ImaginaryI]\ \[Kappa]\ \[Omega] - 
            0.000027164252792063974`\ \[ImaginaryI]\ G\^2\ Re\^2\ \[Kappa]\ \
\[Omega], 
          2.653649615928378`\/Re, \(3.385449580439322`\ \[Kappa]\)\/Re + 
            6.972702837207759`*^-6\ G\^2\ Re\ \[Kappa] + 
            0.0005244416001394039`\ G\ Re\ \[Kappa]\ \[Omega]}, \
{\(0.02710921267809349`\ \[Kappa]\)\/Re - 
            0.00006568002178707814`\ G\^2\ Re\ \[Kappa] - 
            0.00040545391664440714`\ G\ Re\ \[Kappa]\ \[Omega], 
          4.893990214041299`\/Re, 
          0.03433072433772288`\ \[ImaginaryI]\ G\ \[Kappa] + 
            0.15069526905030184`\ \[ImaginaryI]\ \[Kappa]\ \[Omega], 
          0}, {\(-0.048344149057053885`\)\ \[ImaginaryI]\ G\ \[Kappa] + 
            1.907691318680299`*^-6\ \[ImaginaryI]\ G\^3\ Re\^2\ \[Kappa] + 
            0.009689975253410067`\ \[ImaginaryI]\ Re\ \[Epsilon]\ \[Kappa] + 
            0.05421842535618698`\ \[ImaginaryI]\ \[Kappa]\ \[Omega] + 
            0.000012178767275970296`\ \[ImaginaryI]\ G\^2\ Re\^2\ \[Kappa]\ \
\[Omega], 
          0.1666666666666667`\ \[ImaginaryI]\ G, \(2.212503516103493`\ \
\[Kappa]\)\/Re + 0.0002476649474886485`\ G\^2\ Re\ \[Kappa] + 
            0.0015469650912364437`\ G\ Re\ \[Kappa]\ \[Omega], 
          31.36647587353848`\/Re}}}\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Eigenvalues[\(Inverse[Last[#] . First[#]] &\)[
        mat /. {\[Kappa] \[Rule] 1}]]\)], "Input"],

Cell[BoxData[
    \({\(-3.636589561775901`\)\ Re, \(-1.1305185062838263`\)\ Re, \
\(-0.4453079845858082`\)\ Re, \(-0.014922888610218732`\)\ Re}\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell["\:0424\:0443\:043d\:043a\:0446\:0438\:0438 \:043d\:0430\:0445\:043e\
\:0436\:0434\:0435\:043d\:0438\:044f \:0438\:043d\:043a\:0440\:0435\:043c\
\:0435\:043d\:0442\:043e\:0432", "Subsection"],

Cell[CellGroupData[{

Cell["\<\
\:041f\:043e\:043b\:0443\:0447\:0435\:043d\:0438\:0435 \:0441.\:0437. \:0438 \
\:0441.\:0432. \:0441 \:043f\:043e\:043c\:043e\:0449\:044c\:044e \
Eigen...[Inverse[a].m] (\:043c\:0435\:043d\:0435\:0435 \:0443\:0441\:0442\
\:043e\:0439\:0447\:0438\:0432\:043e)\
\>", "Subsubsection"],

Cell[BoxData[
    \(\(GetIncrements[n_, m_, k1_, R1_] := 
        Eigenvalues[\(Inverse[Last[#]] . First[#] &\)[
            N[FiniteMatrix4Eigen[n, m, k \[Rule] k1, 
                R \[Rule] R1]]]];\)\)], "Input"],

Cell[BoxData[
    \(\(GetEigenWave[n1_, m_, k1_, R1_, mode_:  1] := 
        Block[{eigval, eigvec, nom, syst}, 
          syst = \(Inverse[Last[#]] . First[#] &\)[
              N[FiniteMatrix4Eigen[n1, m, k \[Rule] k1, 
                  R \[Rule] R1]]]; \[IndentingNewLine]{eigval, eigvec} = 
            Select[Transpose[Eigensystem[syst]], NumericQ[First[#]] &] // 
              Transpose; \[IndentingNewLine]nom = 
            Flatten[Position[
                  eigval, \(Sort[eigval, 
                      Re[#1] > Re[#2] &]\)\[LeftDoubleBracket]
                    mode\[RightDoubleBracket]]] // 
              First; \[IndentingNewLine]Print["\<Main eigen value is \>", 
            eigval[\([nom]\)]]; \[IndentingNewLine]Return[
            eigvec\[LeftDoubleBracket]
              nom\[RightDoubleBracket]];];\)\)], "Input"]
}, Open  ]],

Cell[CellGroupData[{

Cell["\<\
\:041f\:043e\:043b\:0443\:0447\:0435\:043d\:0438\:0435 \:0441.\:0437. \:0438 \
\:0441.\:0432. \:0441 \:043f\:043e\:043c\:043e\:0449\:044c\:044e \
Eigen...[{m,a}]\
\>", "Subsubsection"],

Cell[BoxData[
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        Select[Eigenvalues[mat[Re1]], NumericQ];\)\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(\(GetEigenWaveM[syst_, mode_:  1] := 
        Block[{eigval, eigvec, nom}, \[IndentingNewLine]{eigval, eigvec} = 
            Select[Transpose[Eigensystem[syst]], NumericQ[First[#]] &] // 
              Transpose; \[IndentingNewLine]nom = 
            Flatten[Position[
                  eigval, \(Sort[eigval, 
                      Re[#1] > Re[#2] &]\)\[LeftDoubleBracket]
                    mode\[RightDoubleBracket]]] // 
              First; \[IndentingNewLine]Print["\<Main eigen value is \>", 
            eigval[\([nom]\)]]; \[IndentingNewLine]Return[
            eigvec\[LeftDoubleBracket]
              nom\[RightDoubleBracket]];];\)\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(\(GetIncrements[nr_, n\[Phi]_, \[Kappa]1_, R1_, subst___] := 
        Select[Eigenvalues[
            N[FiniteMatrix4Eigen[nr, n\[Phi], 
                subst, \[Kappa] \[Rule] \[Kappa]1, 
                R \[Rule] R1, \[Omega] \[Rule] 0, \[Epsilon] \[Rule] 0, 
                G \[Rule] 4]]], NumericQ];\)\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(\(GetEigenWave[n1_, m_, k1_, R1_, mode_:  1] := 
        Block[{eigval, eigvec, nom, syst}, 
          syst = N[
              FiniteMatrix4Eigen[n1, m, k \[Rule] k1, 
                R \[Rule] R1, \[Omega] \[Rule] 0, \[Epsilon] \[Rule] 0, 
                G \[Rule] 4]]; \[IndentingNewLine]{eigval, eigvec} = 
            Select[Transpose[Eigensystem[syst]], NumericQ[First[#]] &] // 
              Transpose; \[IndentingNewLine]nom = 
            Flatten[Position[
                  eigval, \(Sort[eigval, 
                      Re[#1] > Re[#2] &]\)\[LeftDoubleBracket]
                    mode\[RightDoubleBracket]]] // 
              First; \[IndentingNewLine]Print["\<Main eigen value is \>", 
            eigval[\([nom]\)]]; \[IndentingNewLine]Return[
            eigvec\[LeftDoubleBracket]
              nom\[RightDoubleBracket]];];\)\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(\(GetMainIncrement[n_, m_, k1_, R1_, 
          num_:  1] :=  (*\(GetMainIncrement[n, k1, R1, 
              num]\)\(=\)*) \((Print[{n, k1, R1}]; 
          Take[Sort[Re /@ GetIncrementsM[mat[R1]]], {\(-num\)}] // 
            First)\);\)\)], "Input",
  InitializationCell->True]
}, Open  ]],

Cell[CellGroupData[{

Cell["\:041f\:0440\:043e\:0432\:0435\:0440\:043a\:0438", "Subsubsection"],

Cell[BoxData[
    \(Take[Sort[GetIncrements[20, 0, 1, 100], Re[#1] > Re[#2] &], 
      10]\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(GetMainIncrement[100, 0, 1, 100, 2]\)], "Input"],

Cell[BoxData[
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Cell[BoxData[
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}, Open  ]],

Cell[BoxData[
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\ \:043e\:043f\:0440\:0435\:0434\:0435\:043b\:0438\:0442\:0435\:043b\:0435\ \
\:043f\:043e\:0441\:043b\:0435\ \:043f\:043e\:0434\:0441\:0442\:0430\:043d\
\:043e\:0432\:043a\:0438\ \:0441\:043e\:0431\:0441\:0442\:0432\:0435\:043d\
\:043d\:043e\:0433\:043e\ \:0437\:043d\:0430\:0447\:0435\:043d\:0438\:044f\
\[IndentingNewLine]With[{n2 = 3, m = 0, k2 = 1, R2 = 100, 
            mod = 1}, \(Det[
                SetPrecision[
                  First[#] - \(Sort[GetIncrements[n2, m, k2, R2], 
                          Re[#1] > Re[#2] &]\)[\([mod]\)] Last[#], 1000]] &\)[
            SetPrecision[
              FiniteMatrix4Eigen[n2, m, k \[Rule] k2, R \[Rule] R2], 
              1000]]]*) \)], "Input"],

Cell[BoxData[
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\:0432\ \:0432\:0435\:043a\:0442\:043e\:0440\:0435\ \:043f\:043e\:0441\:043b\
\:0435\ \:043f\:043e\:0434\:0441\:0442\:0430\:043d\:043e\:0432\:043a\:0438\ \
\:0441\:043e\:0431\:0441\:0442\:0432\:0435\:043d\:043d\:044b\:0445\ \:0437\
\:043d\:0430\:0447\:0435\:043d\:0438\:0439\ \:0438\ \:0432\:0435\:043a\:0442\
\:043e\:0440\:043e\:0432*) \)\(\[IndentingNewLine]\)\(\(With[{n2 = 300, 
              m = 0, k2 = 1, R2 = 1000, 
              mod = 2}, \(\((First[#] - \(Sort[GetIncrements[n2, m, k2, R2], 
                            Re[#1] > Re[#2] &]\)[\([mod]\)] Last[#])\) . 
                  GetEigenWave[n2, m, k2, R2, mod] &\)[
              FiniteMatrix4Eigen[n2, m, k \[Rule] k2, R \[Rule] R2]]] // 
          Abs\) // PrintRange;\)\)\)], "Input"]
}, Closed]],

Cell[CellGroupData[{

Cell[BoxData[
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